Ultrasonic Mass Fuel Flow Meter

ABSTRACT

The subject matter of this specification can be embodied in, among other things, a sensor that includes a first axial sensor housing portion having a first cross-sectional area, a second axial sensor housing portion arranged adjacent to the first axial sensor housing portion along the sensor axis and having a second cross-sectional area larger than the first cross-sectional area, and a face extending from the interior surface of the first axial sensor housing portion to the interior surface of the second axial sensor housing portion, a first buffer rod within the first axial sensor housing portion and having a first axial end and a second axial end, a second buffer rod within the second axial sensor housing portion and abutting the face, and having a third axial end and a fourth axial end, and an acoustic transceiver element acoustically mated to the second axial end and the third axial end.

CROSS-REFERENCE TO RELATED PATENT APPLICATIONS

This application claims the benefit of priority to U.S. ProvisionalApplication No. 63/162,359, filed Mar. 17, 2021, the contents of whichare incorporated by reference herein.

TECHNICAL FIELD

This instant specification relates to ultrasonic fluid mass flowsensors.

BACKGROUND

Fluid measurement devices are used for the characterization andoperation of fluid control systems. As the dynamic bandwidths, flowranges, accuracies, and reliabilities of flow measurement devicesimprove, the potential application landscape of such devices broadens.High dynamic bandwidth flow meters can be used as control systemfeedback sensors for improving steady state and/or transient accuracy infuel systems. Ultrasonic flow meters (USFM) are a proven industrialtechnology that can be leveraged for implementation to aircraft turbinesystems.

Existing time of flight ultrasonic flow meters are used in the racingand automotive industries, pipeline custody transfer, industrial flowmeasurement, and many other applications. However, many of theseapplications encompass steady-state flow conditions, and theirrespective applications allow for volumetric flow measurement. In otherapplications, such as aircraft gas turbine engine applications, thefluid environmental conditions of the fuel delivery system imposessignificant design challenges.

SUMMARY

In general, this document describes ultrasonic fluid mass flow sensors.

In an example embodiment, a sensor includes a sensor housing having aninterior surface defining a sensor axis and an axial interior sensorhousing cavity including a first axial sensor housing portion having afirst cross-sectional area perpendicular to the sensor axis, a secondaxial sensor housing portion arranged adjacent to the first axial sensorhousing portion along the sensor axis and having a secondcross-sectional area larger than the first cross-sectional areaperpendicular to the sensor axis, and a face extending from the interiorsurface of the first axial sensor housing portion to the interiorsurface of the second axial sensor housing portion, a first axial bufferrod arranged within the first axial sensor housing portion and having afirst axial end and a second axial end, a second axial buffer rodarranged within the second axial sensor housing portion and abutting theface, and having a third axial end and a fourth axial end, and anacoustic transceiver element acoustically mated to the second axial endand the third axial end.

Various embodiments can include some, all, or none of the followingfeatures. The acoustic transceiver element can be configured to emit avibration having a predetermined wavelength (A), and the first axialbuffer rod and the second axial buffer rod both can have axial lengthsof about a round multiple of n/2 λ. The sensor can include a tubularfluid conduit having a first end and a second end opposite the first endand defining a conduit axis, arranged such that the conduit axis issubstantially aligned with the sensor axis. The sensor can includeanother sensor housing having another interior surface defining anothersensor axis and another axial interior sensor housing cavity havinganother first axial sensor housing portion having another firstcross-sectional area perpendicular to the other sensor axis, anothersecond axial sensor housing portion arranged adjacent to the other firstaxial sensor housing portion along the other sensor axis and havinganother second cross-sectional area larger than the other firstcross-sectional area perpendicular to the other sensor axis, and anotherface extending from the other interior surface of the other first axialhousing portion to the other interior surface of the other secondhousing portion, another first axial buffer rod arranged within theother first housing portion and having another first axial end andanother second axial end, another second axial buffer rod arrangedwithin the other second housing portion and abutting the other face, andhaving another third axial end and another fourth axial end, and anotheracoustic transceiver element acoustically mated to the other secondaxial end and the other third axial end, wherein the other sensor axisis substantially aligned with the conduit axis. The sensor of claim caninclude a fluid housing having a fluid housing interior surface definingan axial fluid housing cavity, a first fluid port in fluidiccommunication with the axial fluid housing cavity, and a second fluidport in fluidic communication with the axial fluid housing cavity,wherein the tubular fluid conduit is in fluidic communication with thesecond fluid port and extends axially away from the fluid housing alongthe conduit axis at the first end, and the sensor housing is arrangedwithin the first fluid housing such that the sensor axis issubstantially aligned with the conduit axis. The sensor can includeanother sensor housing having another interior surface defining anothersensor axis and another axial interior sensor housing cavity havinganother first axial sensor housing portion having another firstcross-sectional area perpendicular to the other sensor axis, anothersecond axial sensor housing portion arranged adjacent to the other firstaxial sensor housing portion along the other sensor axis and havinganother second cross-sectional area larger than the other firstcross-sectional area perpendicular to the other sensor axis, and anotherface extending from the other interior surface of the other first axialhousing portion to the other interior surface of the other secondhousing portion, another first axial buffer rod arranged within theother first housing portion and having another first axial end andanother second axial end, another second axial buffer rod arrangedwithin the other second housing portion and abutting the other face, andhaving another third axial end and another fourth axial end, anotheracoustic transceiver element acoustically mated to the other secondaxial end and the other third axial end, and another fluid housinghaving another fluid housing interior surface defining another axialfluid housing cavity, another first fluid port in fluidic communicationwith the other axial fluid housing cavity, and another second fluid portin fluidic communication with the other axial fluid housing cavity,wherein the tubular fluid conduit is in fluidic communication with theother second fluid port and extends axially away from the other fluidhousing along the conduit axis at the second end, and the other sensorhousing is arranged within the other first fluid housing such that theother sensor axis is substantially aligned with the conduit axis. Theacoustic transceiver element can include a piezoelectric element. Thesensor can include a matching layer affixed to the fourth axial end andhaving a thickness of about (2n-1)λ/4, where n>0. The first axial endcan define an acoustic reflector. The first axial end is abutted to agas or an at least partial vacuum.

In another example embodiment, a sensor system includes a fluid housinghaving a first fluid housing portion defining a first axial fluidhousing cavity and having a first fluid port in fluidic communicationwith the first axial fluid housing cavity, a second fluid housingportion defining a second axial fluid housing cavity and having a secondfluid port in fluidic communication with the second axial fluid housingcavity, and a tubular fluid conduit in fluidic communication with thefirst fluid port at a first end and in fluidic communication with thesecond fluid port at a second end opposite the first end, and defining aconduit axis, a first acoustic transceiver element arranged within thefirst axial fluid housing cavity, axially aligned with the conduit axis,and a second acoustic transceiver element arranged within the secondaxial fluid housing cavity, axially aligned with the conduit axis.

Various embodiments can include some, all, or none of the followingfeatures. The sensor system can include circuitry configured to activatethe first acoustic transceiver element to emit a first incident wave,activate the second acoustic transceiver element to emit a secondincident wave, detect, by the first acoustic transceiver element, anecho of the first incident wave, determine a fluid acoustic impedance ofa fluid in the tubular fluid conduit based on the echo, detect, by thesecond acoustic transceiver element, at least a first portion of thefirst incident wave, determine a first time of flight of the portion ofthe first portion, detect, by the first acoustic transceiver element, atleast a second portion of the second incident wave, determine a secondtime of flight of the second portion, and determine a mass fluid flowrate based on the determined fluid acoustic impedance, the determinedfirst time of flight, and the determined second time of flight. One orboth of the first acoustic transceiver element or the second acoustictransceiver element can each include a sensor housing having an interiorsurface defining a sensor axis and an axial interior sensor housingcavity having a first axial sensor housing portion having a firstcross-sectional area perpendicular to the sensor axis, a second axialsensor housing portion arranged adjacent to the first axial sensorhousing portion along the sensor axis and having a secondcross-sectional area larger than the first cross-sectional areaperpendicular to the sensor axis, and a face extending from the interiorsurface of the first axial sensor housing portion to the interiorsurface of the second axial sensor housing portion, a first axial bufferrod arranged within the first axial sensor housing portion and having afirst axial end and a second axial end, a second axial buffer rodarranged within the second axial sensor housing portion and abutting theface, and having a third axial end and a fourth axial end, and anacoustic transceiver element acoustically mated to the second axial endand the third axial end. The acoustic transceiver element can beconfigured to emit a vibration having a predetermined wavelength (λ),and the first axial buffer rod and the second axial buffer rod can bothhave axial lengths of about a round multiple of n/2 λ. The acoustictransceiver element can include a piezo element. The sensor system caninclude a matching layer affixed to the fourth end and having athickness of about an odd multiple of ¼ λ. The first axial end candefine an acoustic reflector. The first axial end can be abutted to agas or an at least partial vacuum.

In an example implementation, a method of sensing includes activating afirst emitter to emit at least a first incident wave in a firstdirection and emit a second incident wave in a second direction oppositethe first direction, transmitting the first incident wave along a firstbuffer rod having a first axial end abutted to the first emitter and asecond axial end opposite the first axial end, transmitting the secondincident wave along a second buffer rod having a third axial end abuttedto the first emitter and a fourth axial end opposite the third axialend, reflecting a first echo of the first incident wave by a firstacoustic reflector defined along a portion of the second axial end,detecting the first echo, determining a first amplitude of the firstecho, reflecting a second echo of the second incident wave by the fourthaxial end, detecting the second echo, determining a second amplitude ofthe second echo, and determining a reflection coefficient based on thefirst amplitude and the second amplitude.

Various implementations can include some, all, or none of the followingfeatures. The method can include determining a fluid acoustic impedanceof a fluid at the second axial end based on the determined reflectioncoefficient and a predetermined buffer rod acoustic impedance. Themethod can include transmitting, at the second axial end, a portion ofthe first incident wave through the fluid to a first sensor arranged apredetermined distance away from and opposite the first emitter, whereinthe fluid is within a tubular fluid conduit having a predeterminedcross-sectional area, detecting, by the first sensor, the portion of thefirst incident wave, determining, based on the detected portion of thefirst incident wave, a first time of flight of the portion of the firstincident wave, transmitting, by a second emitter, another first incidentwave through the fluid to a second sensor proximal to the first emitter,detecting, by the second sensor, the other first incident wave, anddetermining, based on the detected other first incident wave, a secondtime of flight of the other first incident wave. The method can includedetermining at least one of a velocity of the fluid within the tubularfluid conduit or a speed of sound within the fluid based on the firsttime of flight, the second time of flight, and the predetermineddistance. The method can include determining a mass fluid flow ratebased on the predetermined cross-sectional area, and the determinedspeed of sound. The mass fluid flow rate can be given by the equation:

$m_{fluid} = {{\left( \frac{V_{fluid}}{C_{fluid}} \right) \times C_{d} \times A \times Z_{fluid}} = {\left( \frac{t_{up} - t_{dn}}{t_{up} + t_{dn}} \right) \times C_{d} \times A \times {\left( \frac{Z_{buffer}\left( {1 - R} \right)}{1 + R} \right).}}}$

One or both of the first emitter and the first sensor can be piezoelements. A piezo element can include the first emitter and the firstsensor. The first acoustic reflector can include a matching layeraffixed to the fourth axial end and having a thickness of (2n-1) λ/4,where n>0. The first axial end can be abutted to a gas or an at leastpartial vacuum.

In another example implementation, a method of protecting a sensorelement includes providing a sensor having a sensor housing having aninterior surface defining a sensor axis and an axial interior sensorhousing cavity having a first axial sensor housing portion having afirst cross-sectional area perpendicular to the sensor axis, a secondaxial sensor housing portion arranged adjacent to the first axial sensorhousing portion along the sensor axis and having a secondcross-sectional area larger than the first cross-sectional areaperpendicular to the sensor axis, and a face extending from the interiorsurface of the first axial sensor housing portion to the interiorsurface of the second axial sensor housing portion, a first axial bufferrod arranged within the first axial sensor housing portion and having afirst axial end and a second axial end, a second axial buffer rodarranged within the second axial sensor housing portion and abutting theface, and having a third axial end and a fourth axial end, and anacoustic transceiver element acoustically mated to the second axial endand the third axial end, providing a fluid at fourth axial end, andblocking, by the second axial buffer rod and the sensor housing, fluidflow from the fourth axial end to the acoustic transceiver element.

Various implementations can include some, all, or none of the followingfeatures. The method can include applying fluid pressure against thefourth axial end to produce an axial force against the first axialbuffer rod, transmitting, by the second axial buffer rod, the axialforce to the sensor housing, and preventing, by the sensor housing,transmission of the axial force to the acoustic transceiver element. Themethod can include transmitting, by the second axial portion, the axialforce to the face, wherein the face interferes with axial movement ofthe second axial buffer rod toward the acoustic transceiver element.

The systems and techniques described here may provide one or more of thefollowing advantages. First, a system can provide improved environmentalsurvivability against wide fluid temperature ranges. Second, the systemcan provide improved environmental survivability against wide fluidpressure ranges. Third, the system can provide improved environmentalsurvivability against harsh fluids. Fourth, the system can provideintegral fluid density sensing. Fifth, the system can be relativelyunaffected by fluid flow dynamics (e.g., swirl, vortices, instability).Sixth, the system can be used with update rates of 100 Hz or greater,while maintaining accuracy.

The details of one or more implementations are set forth in theaccompanying drawings and the description below. Other features andadvantages will be apparent from the description and drawings, and fromthe claims.

DESCRIPTION OF DRAWINGS

FIG. 1 is a cross-sectional diagram an example of an ultrasonic flowmeasurement system.

FIG. 2 is a cross-sectional diagram of an example ultrasonic sensormodule of the system of FIG. 1.

FIG. 3 shows a conceptual example of incident and reflected wavepropagation in the module of FIG. 2.

FIG. 4 shows a conceptual example of fluid pressure mitigation in themodule of FIG. 2.

FIGS. 5A-5C show conceptual examples of incident wave traversal in anultrasonic flow measurement system.

FIGS. 6A and 6B are graphs that show example incident waves and echoesin the ultrasonic flow measurement system of FIG. 1.

FIG. 7 is a flow chart that shows an example of a process fordetermining a fluid reflection coefficient.

FIG. 8 is a flow chart that shows an example of a process fordetermining a mass fluid flow.

FIG. 9 is a flow chart that shows an example of a process for resistingeffects of fluid exposure on the acoustic transducer of the module ofFIG. 2.

FIG. 10 is a schematic diagram of an example of a generic computersystem.

DETAILED DESCRIPTION

This document describes ultrasonic fluid mass flow sensor (USFM)systems, and techniques for measuring fluid flow characteristics offluids. In general, the USFM systems described in this system can beused in fluid environments that would degrade or destroy existing USFMs.The fluid environmental conditions of fuel delivery systems can imposesignificant design challenges. For current, state of the art, aircraftand other gas turbine engine applications, an ultrasound transducerdeployed for such applications will be expected to survive high fluidpressures (e.g., 0 psi to 4000 psi or higher) and a wide range of fluidtemperatures, including high fluid temperatures (e.g., −65 degrees F. orlower to 325 degrees F. or higher).

These temperatures and pressures are far more challenging than thoserequired in typical industrial fluid, steam, or pipeline custodytransfer applications. To remain effective in such applications, awetted transducer must also not be degraded by long-term immersion incaustic fluids such as aircraft fuels and/or additives at hightemperatures and/or pressures. The USFM systems described in thisdocument include features that improve the survivability of the USFMunder such conditions.

In existing industrial and custody transfer USFMs based on time offlight, cross-correlation, and phase shift measurements have accuracylimitations determined by the flow velocity range, or turn-down ratio,within the flow measurement volume. For example, during low flowconditions the difference between upstream and downstream measurementscan be too insensitive to maintain a target accuracy. During high flowconditions, measurement accuracy can suffer from flow instabilities,often caused by the acoustic path being off-axis with respect to theflow, flow separation, and/or non-axisymmetric flow conditions. Off-axistransducer configurations can also cause sensitivity and accuracyproblems. Round transducers can impose non-uniform ultrasound fields asthe waves pass diagonally through the flow, reducing accuracy. Inexisting USFMs having ultrasound beams smaller than the flowcross-section, the full flow profile is not insonified and thereforemust be estimated, typically with a single K-factor correction value, ora complex coefficient matrix for USFMs using multiple sonic paths, suchas in natural gas custody transfer applications. In existing USFMdesigns, flow measurement accuracy can be difficult to maintain over alarge turndown ratio when the flow regime is unstable, or changessubstantially from laminar to turbulent flow. For example, some existingindustrial USFMs have a practical turndown ratio of no more than 50:1while maintaining accuracy, even when application piping and flowconditioning are executed ideally. By comparison, a gas turbine fuelsystem can require a substantially higher turndown of generally 100:1,with some applications upward of 350:1 or more. In addition, a gasturbine flow measurement system must be capable of maintaining dynamicaccuracy, with update rates of 100 Hz or more.

Mass flow is critical to the combustion process to maintain a safe andoperable fuel to air ratio. Excess fuel to air ratio can lead tocompressor surge or over temperature events. Conversely, excess air tofuel can lead to compressor blow out. Either of these events can bedetrimental to gas turbine performance and are therefore key designdrivers for gas turbine engine design. Additionally, some applicationssuch as gas turbine engines are designed to operate on various fueltypes under varying pressures and temperatures.

An important variable, especially in aircraft gas turbine applications,is the variation in fuel specific gravity amidst the fuel types andtemperatures. In some applications, the expected fuel specific gravitycan vary by approximately 25% across expected temperature ranges anduseable fuel types. The wide range in fuel density, if unknown, willdrive a broad range in mass fuel flow for a given volumetric flow rate.This variability can lead to large variances in mass air to fuel flowratios, making engine design across the environmental range inefficient,yielding oversized engines, conservative acceleration and/ordeceleration schedules, excessive surge margins, and/or excessiveblowout margins.

FIG. 1 is a cross-sectional diagram of an example of an ultrasonic flowmeasurement (USFM) system 100. The USFM system 100 includes a fluidhousing 110 and two ultrasonic sensor modules 200. The fluid housing 110includes an axial fluid housing cavity 120 a defined by an interiorsurface 121 a, and an axial fluid housing cavity 120 b defined by aninterior surface 121 b. A fluid port 122 a defines a fluid path 124 aconnected to the fluid cavity 120 a. A fluid port 122 b defines a fluidpath 124 b connected to the fluid cavity 120 b. The fluid housing 110also defines a cavity 126 that extends between the fluid cavity 120 aand the 120 b.

The fluid housing 110 also includes a fluid control conduit 130 thatdefines a fluid path 132 along a conduit axis 134. The fluid controlconduit 130 fluidically connects the fluid cavity 120 a and the fluidcavity 120 b, putting the fluid cavity 120 a in fluidic communicationwith the fluid cavity 120 b. The fluid control conduit 130 has apredetermined flowable area 136 and shape (e.g., square, tapered, and/orcurved edges, parallel or tapered walls, to affect fluid flow behavior).In some implementations, the fluid housing 110 can be used across manyapplications, and the fluid control conduit 130 can be aninterchangeable, specialized subcomponent (e.g., an adapter) that canadapt the USFM system 100 for particular fluid types, applications,and/or operational conditions.

Referring now to FIG. 2, an enlarged cross-sectional diagram of theexample ultrasonic sensor module 200 of the system of FIG. 1 is shown.The ultrasonic sensor module 200 includes a sensor housing 202 having anaxial interior sensor housing cavity 204 and a sensor axis 206 definedby an interior surface 207. When the ultrasonic sensor module 200 isassembled to the fluid housing 110 of FIG. 1, the sensor axis 206 issubstantially aligned with the conduit axis 134. The sensor housing 202has an axial sensor housing portion 208 a having a cross-sectional area209 a perpendicular to the sensor axis 206. The sensor housing 202 alsohas an axial sensor housing portion 208 b having a cross-sectional area209 b perpendicular to the sensor axis 206. The cross-sectional area 209b is dimensionally larger than the cross-sectional area 209 a. A face210 extends from the interior surface 207 of the axial sensor housingportion 208 a to the interior surface 208 of the axial sensor housingportion 208 b. In the illustrated example, the face 210 is formed as asubstantially squared shoulder or ledge at the transition between thecross-sectional area 209 a and the cross-sectional area 209 b. In someembodiments, the face 210 can be a tapered or otherwise non-squaredtransition between the cross-sectional area 209 a and thecross-sectional area 209 b.

The ultrasonic sensor module 200 also includes an acoustic transceiverelement 230. The acoustic transceiver element 230 is configured to emitacoustic vibrations (e.g., ultrasonic sounds waves) at a predeterminedwavelength (A) when energized. In some embodiments, a separate acousticdriver and acoustic receiver may be implemented as the acoustictransceiver element 230. In some embodiments, the acoustic transceiverelement 230 can be configured to also detect received acousticvibrations. In some embodiments, the acoustic transceiver element 230can be a piezo element.

The acoustic transceiver element 230 is arranged between an axial bufferrod 250 and an axial buffer rod 270. A face 231 of the acoustictransceiver element 230 is acoustically mated or otherwise abutted to anaxial end 252 of the buffer rod 250 by a bonding layer 232. A face 233of the acoustic transceiver element 230, opposite the face 231, isacoustically mated or otherwise abutted to an axial end 272 of thebuffer rod 270 by a bonding layer 234. In some embodiments, the bondinglayers 232 and 234 can be adhesive layers.

In some embodiments, the buffer rods 250 and 270 can be made of anyappropriate material or combination of materials that can provide properacoustic impedance ratios when combined with matching layer material toimprove or maximize sensitivity of measurements, are cost effective, canbe fabricated within reasonable manufacturing tolerances, and/or providegood mechanical and chemical compatibility in the intended applicationenvironment. Examples of buffer rod materials include titanium alloys,austenitic stainless steel, aluminum, borosilicate glasses, fused (e.g.,non-crystalline) quartz, and technical ceramics (e.g., AlN, Al₃O₃, SiN,and blends).

In some embodiments, the bonding layers 232 and/or 234 can be omitted,with the acoustic transceiver element 230 in direct contact with theaxial ends 252 and/or 272. For example, the acoustic transceiver element230 can be held in place by mechanically capturing the acoustictransceiver element 230 between the axial buffer rods 250 and 270, orthe acoustic transceiver element 230 can be held in place by fixationfeatures formed in the interior surface 207. In some embodiments, thebonding layers 232 and/or 234 can be formed from a highly ductilematerial, such as gold or lead, which can be conformed to the matingfaces of the acoustic transceiver element 230 and the axial ends 252 and272.

The axial buffer rod 250 extends along the sensor axis 206 from theaxial end 252 to an axial end 254 opposite the axial end 252. The axialbuffer rod 250 has a predetermined axial length of about a roundmultiple of one-half of the transmission wavelength of the acoustictransceiver element 230 (n/2 λ). In some embodiments in which longbuffer rods are used (e.g., where n is greater than about 10), thepredetermined axial lengths may not need to be configured with roundmultiples of the one-half wavelength. In some embodiments, the axialbuffer rod 250 can contact the interior surface 203 directly orindirectly (e.g., through a seal, sleeve, or bonding material) tosubstantially seal the sensor cavity 204 and the acoustic transceiverelement 230 from fluid incursion at the axial end 254.

The axial buffer rod 270 extends along the sensor axis 206 from theaxial end 272 to an axial end 274 opposite the axial end 272. The axialbuffer rod 270 has a predetermined axial length of about a roundmultiple of one-half of the transmission wavelength of the acoustictransceiver element 230 (n/2 λ). In some embodiments, the axial bufferrod 270 can contact the interior surface 207 directly or indirectly(e.g., through a seal, sleeve, potting, or bonding material) tosubstantially seal the sensor cavity 204 and the acoustic transceiverelement 230 from fluid incursion at the axial end 254, and/or to enhancethe robustness of the USFM module 200.

The buffer rods 250 and 270 have predetermined acoustic impedances(Z_(buffer)). In the illustrated example, the cavity 204 is filled witha gas, such as air, or a partial vacuum. In some embodiments, theacoustic impedance of the content (e.g., medium) of the cavity can be atleast 1000× lower than that of the buffer rod over the operatingtemperature range of the sensor. The acoustic impedance of the cavity issufficiently different from the acoustic impedance of the buffer rod 270to reflect an acoustic echo when struck by an acoustic wave (e.g., anultrasonic ping). In some embodiments, the cavity 204 can be evacuatedto form at least a partial vacuum. The axial end 254 forms part of thefluid conduit 130 of FIG. 1, which in use is filled with a fluid (e.g.,fuel) having an acoustic impedance that is sufficiently different fromthe acoustic impedance of the buffer rod 250 to reflect an acoustic echowhen struck by an acoustic wave (e.g., an ultrasonic ping).

In some embodiments, portions of the buffer rods 250 and/or 270 mayinclude a cladding. For example, the cladding can be configured toimprove the efficiency and/or sensitivity of the ultrasonic sensormodule 200 by directing the propagation of incident waves, acousticallyand/or electrically isolating the buffer rods 250 and 270 from thesensor housing 202, and/or thermally insulating the buffer rods 250 and270 from the sensor housing 202.

Still referring to FIG. 2, the ultrasonic sensor module 200 includes amatching layer 280 acoustically mated with, affixed to, or otherwiseabutted to the axial end 254 of the buffer rod 250. In some embodiments,the matching layer 280 may be adhered to the axial end 254. In someembodiments, portions of the matching layer 280 may extend to the sensorhousing 202 and be affixed (e.g., welded) to the sensor housing 202. Insome embodiments in which the matching layer 280 is affixed to thesensor housing 202, the joint between the matching layer 280 and thesensor housing 202 can substantially seal the sensor cavity 204 fromfluid incursion at the axial end 254. The matching layer 280 has anaxial thickness that is about a round odd multiple of the transmissionwavelength of the acoustic transceiver element 230 (e.g., (2n−1)λ/4where n>0), for example ¼ λ.

In some embodiments, the matching layer 280 can increase reflectionsensitivity, improving or maximizing the rate of change of reflectioncoefficient with respect to change in fluid impedance, d_(R)/dZ_(fluid),e.g., as fuel changes temperature, Z_(fluid) changes and therefore thereflection ratio changes. In some embodiments, the use of two or more ¼wave discrete matching layers, a multilayer ¼ wave graded compositematching layer, or a multilayer thin film ¼ wave matching layer, alongwith the optional inclusion of a non-acoustic (e.g., < 1/10 wave) wearplate can provide additional reflection sensitivity above thatobtainable with a single matching layer

Referring again to FIG. 1, the two ultrasonic sensor modules 200 faceeach other across the fluid control conduit 130. The acoustic transducerelements of the ultrasonic sensor modules 200 are separated by apredetermined distance 150.

The USFM system 100 includes a controller 190. The controller 190includes circuitry configured to activate the ultrasonic sensor modules200 to cause acoustic incident waves to be emitted, to detect thereception of acoustic waves at the ultrasonic sensor modules 200,measure the timings and/or amplitudes between transmission and receptionof various combinations of direct and reflected acoustic waves, and/ordetermine various properties of the USFM system 100 and/or the fluidbased in part on those measured timings as will be discussed further inthe descriptions of FIGS. 3-9.

In use, a fluid is flowed through the USFM system 100. For example, afluid such as fuel can be provided at the fluid port 122 a where it willflow along the fluid path 124 a into the fluid cavity 120 a. The fluidflows around the ultrasonic sensor module 200 to the fluid controlconduit 130. The fluid flows through the fluid control conduit 130 alongthe fluid path 132 and then flows around the ultrasonic sensor module200 to the fluid cavity 120 b. The fluid then flows along the fluid path124 b out the fluid port 122 b. As will be discussed further in thedescriptions of FIGS. 3-9, the ultrasonic sensor modules 200 areprotected from direct exposure to the fluid, and are used to transmitacoustic waves through the fluid to determine properties of the fluid,such as acoustic impedance and mass flow.

FIG. 3 shows a conceptual example of incident wave propagation in theultrasonic sensor module 200 of FIG. 2. In use, the acoustic transceiverelement 230 is activated to emit an incident wave (e.g., a ping). Theincident wave is emitted from both of the faces 231 and 233. Theincident wave is transmitted into and along the buffer rods 250 and 270.A portion of the incident wave, represented by arrow 310, travelsthrough the axial buffer rod 270 until it encounters the axial end 274.The junction of the axial end 274 and the cavity 204 causes a portion ofthe incident wave 310 to be reflected as an echo represented by arrow320. The echo 320 travels back to be detected by the acoustictransceiver element 230. In some embodiments, the ultrasonic sensormodule 200 may include a separate acoustic emitter and receiver fortransmission and detection of the incident waves.

Another portion of the incident wave, represented by arrow 330, travelsthrough the axial buffer rod 250 until it encounters the axial end 254.The junction of the axial end 254 and a fluid 301 at the matching layer280 (e.g., or at the axial end 254 in embodiments in which the matchinglayer 280 is not used) causes a portion of the incident wave 330 to bereflected as an echo represented by arrow 340. The echo 340 travels backto be detected by the acoustic transceiver element 230.

In some implementations, the time between the transmission of theincident wave and detection of the echo 320 can be measured (e.g., bythe example controller 190 of FIG. 1) to determine a first time offlight. In some implementations, the time between the transmission ofthe incident wave and detection of the echo 340 can be measured todetermine a second time of flight. The amplitudes of the echo 320 andthe echo 340 are measured. As will be discussed further in thedescriptions of FIGS. 6A-7, the measured times-of-flight, the measuredecho amplitudes, and predetermined information about the acousticimpedance of the buffer rods 250 and 270 and the predetermined distancesbetween the acoustic transceiver element 230, the axial end 254, and theaxial end 274, can be used to determine properties of the fluid 301 atthe axial end 254, such as acoustic impedance (Z_(fluid)) and/or speedof sound in the fluid (C_(fluid)).

In some implementations, the ultrasonic sensor module 200 can be used inapplications other than the USFM system 100. For example, the ultrasonicsensor module 200 can be put into contact with a fluid (e.g., attachedto or submerged in a tank, pipe, or other fluid vessel or volume) andcan be sonified as part of a process to determine an acoustic impedanceof the fluid, a speed of sound in the fluid, and/or a fluid density ofthe fluid.

In some implementations, characteristics of the buffer rods 250 and/or270 themselves can be determined based on the measured times-of-flightand/or the measured echo amplitudes (e.g., to calibrate for unknownbuffer rod acoustic impedance and/or compensate for the effects oftemperature changes on the ultrasonic sensor module 200). Similarly, insome implementations, the distances between the acoustic transceiverelement 230 and one or both of the axial end 274 and/or the axial end254 can be determined based on the measured times of flight, themeasured echo amplitudes, known distances, known buffer rod acousticimpedance, and/or known buffer rod temperature.

FIG. 4 shows a conceptual example of fluid pressure mitigation in theultrasonic sensor module 200 of FIG. 2. In use, the ultrasonic sensormodule 200 is at least partly exposed to the fluid 301 at the axial end254. In some embodiments, the temperature or chemical properties of thefluid 301 can be damaging to the acoustic transceiver element 230;therefore, the ultrasonic sensor module 200 is configured to prevent thefluid 301 from coming into direct contact with the acoustic transceiverelement 230. For example, direct or indirect (e.g., though a shim,sleeve, cladding, seal, or sealant) contact between axial buffer rod 250and the axial sensor housing portion 208 b and/or between the buffer rod250 and the face 210 can substantially block fluid flow from the axialend 254 to the acoustic transceiver element 230. In someimplementations, fluid seepage that gets by the buffer rod 250 can bedirected to the sensor cavity 204 without contacting a major face of theacoustic transceiver element 230.

In use, the ultrasonic sensor module 200 is at least partly exposed tofluid pressure, represented by arrows 410, at the axial end 254. Thefluid pressure 410 is a static fluid pressure relative to the dynamicpressures caused by the acoustic signals used by the acoustictransceiver element 230. In some embodiments, direct or indirect (e.g.,through the buffer rod 250) application of the fluid pressure 410 couldcreate a compressive force against the acoustic transceiver element 230that could offset or otherwise negatively affect signals provided by theacoustic transceiver element 230 in response to sensed acoustic signals.In some implementations, such effects can be compensated bymathematically by electrically offsetting the sensor signals in order torecover an approximation of the true signal.

The ultrasonic sensor module 200 is configured to prevent the fluidpressure 410 from affecting the acoustic transceiver element 230. Forexample, the acoustic transceiver element 230 is acoustically mated tothe axial end 252. As such, the acoustic transceiver element 230 is ableto “float” on the buffer rod 250 relative to the sensor housing 202 andnot become compressed by the fluid pressure 410.

The acoustic transceiver element 230 is also protected from the fluidpressure 410 by the mechanical configuration of the buffer rod 250 andthe sensor housing 202. Fluid pressure 410 is applied to the axial end254, which urges movement of the buffer rod 250 into the sensor cavity204. This pressure that urges such movement is represented by arrows420. Movement of the buffer rod 250 is prevented by contact between theaxial buffer rod 250 and the face 210 of the sensor housing 202, asrepresented by arrows 430. As such, the force 420 is prevented fromreaching the acoustic transceiver element 230.

The smaller size of the cross-sectional area 209 a is sized toaccommodate acoustic transceiver element 230 and decouple thermalexpansion of the sensor housing 202 from the acoustic path. The largersize of the cross-sectional area 209 b is sized to accommodate thepressure-induced forces acting on the buffer rod 250. The transmissionof forces into the sensor housing 202 substantially eliminatespressure-induced forces from acting on the acoustic transceiver element230, substantially eliminating the need for pressure compensation,transducer components that are sized to react pressure-induced forces,and/or wetted transducer design constraints.

By decoupling the acoustic transceiver element 230 from the fluidpressure environment, several advantages are observed. For example,fluid/fuel compatibility of the acoustic transceiver element 230 is notrequired. In another example, the acoustic transceiver element 230frequency is not restricted by thickness requirements driven bypressure-induced forces. In another example in which the acoustictransceiver element 230 is a piezo transducer, the piezo thicknessrequired to support fluid pressure puts the operating frequency of theacoustic transceiver element 230 far below operating requirements oftime of flight measurement. In yet another example, the operationalfrequency of the acoustic transceiver element 230 can be sized toimprove acoustic optimization and/or low flow measurement accuracy.

FIGS. 5A-5C show conceptual examples of incident wave traversal in anultrasonic flow measurement system 500. In some implementations, theUSFM system 500 can be an example of the USFM system 100 of FIG. 1. TheUSFM system 500 includes two acoustic emitters 510 a and 510 b, twoacoustic receivers 512 a and -512 b, and a fluid control conduit 520. Afluid flows along the fluid control conduit 520 in a directionrepresented by arrow 501.

The derivation that follows assumes that the acoustic receivers 512 aand 512 b are aligned with their respective acoustic emitters 510 a and510 b, perpendicular to the major axis of the fluid control conduit 520.Therefore, the below derivation omits angles of incidence. If theacoustic emitters 510 a, 510 b and acoustic receivers 512 a, 512 b wereplaced off axis, the following derivation could be re-derived using anangle of incidence. However, for simplicity, the trigonometry used tocompensate for such angles is not used here.

Referring to FIG. 5A, first, the speed of sound traveling through anon-moving fluid is considered:

Distance = Velocity × time Or:Length(L) = Speedofsoundinfluid(C_(fluid)) × time(t)∴ L₁ = C_(fluid) × t₁ $t_{1} = \frac{L_{1}}{C_{fluid}}$

Where Cfuel is the speed of sound in fluid, L₁ is the distance betweenthe acoustic transmitter 510 a and the acoustic receiver 512 a, and t₁is the signal transit time between the acoustic transmitter 510 a andthe acoustic receiver 512 a.

Assuming that the direction 501 in which the control volume (fluid) ismoving is the same as a direction of sound travel, represented by line502 a from the acoustic transmitter 510 a to the acoustic receiver 512a, the speed of the sound wave traveling through the fluid will changerelative to the speed of the fluid.

∴ L₂ = V₂ × t₂ V₂ = V_(fluid) + C_(fluid)∴ L₂ = (V_(fluid) + C_(fluid))t₂$t_{2} = \frac{L_{2}}{\left( {C_{fluid} + V_{fluid}} \right)}$

Where V_(fluid) is the average velocity of moving fluid, L₂ is thedistance between the acoustic transmitter 510 a and the acousticreceiver 512 a, and t₂ is the signal transit time between the acoustictransmitter 510 a and the acoustic receiver 512 a.

Referring now to FIG. 5B, it is assumed that the control volume (fluid)is opposing the direction of the sound travel from the acoustic emitter510 b to the acoustic receiver 512 b, represented by line 502 b. Thespeed of the sound wave traveling through the fluid will change relativeto the speed of the fluid.

∴ L₃ = V₃ × t₃ V₃ = −V_(fluid) + C_(fluid)∴ L₃ = (−V_(fluid) + C_(fluid))t₃$t_{3} = \frac{L_{3}}{\left( {C_{fluid} - V_{fluid}} \right)}$

Where L₃ is the distance between the acoustic emitter 510 b and theacoustic receiver 512 b, and t₃ is the signal transit time between theacoustic emitter 510 b and the acoustic receiver 512 b.

Referring to FIG. 5C, for a particular set of ultrasonic sensors, thedevices can both emit and receive signals. This means that for a pair ofsignals, the following characteristics are shared:

L_(up)=L_(down)=L=distance between emitters;

D=diameter Area of the fluid control conduit 520;

A=cross section area;

C_(fluid)=speed of sound in fluid;

V_(fluid)=velocity of fluid;

P_(fluid)=density of fluid;

Z_(fluid)=Acoustic impedance of fluid.

With the above properties shared, the difference in time between theupstream and downstream signal will allow calculation of various fluidcharacteristics.

Upstream and downstream transit times become:

$t_{up} = \frac{L_{up}}{\left( {C_{fluid} - V_{fluid}} \right)}$$t_{down} = \frac{L_{down}}{\left( {C_{fluid} + V_{fluid}} \right)}$Solvingfort_(up), t_(down), andC_(fluid):$C_{fluid} = \frac{\left( {L_{down} - {t_{down}V_{fluid}}} \right)}{t_{down}}$$C_{fluid} = \frac{\left( {t_{up} + {t_{up}V_{fluid}}} \right)}{t_{up}}$

Since speed of sound is common between the transducers, the speeds ofsound are equal to one another and allows fluid velocity to be found:

C_(fluid) = C_(fluid)$\frac{\left( {L_{down} - {t_{down}V_{fluid}}} \right)}{t_{down}} = \frac{\left( {L_{up} + {t_{up}V_{fluid}}} \right)}{t_{up}}$L_(down)t_(up) − t_(down)t_(up)V_(fluid) = L_(up)t_(down) + t_(up)t_(down)V_(fluid)L_(down)t_(up) − L_(up)t_(down) = t_(up)t_(down)V_(fluid) + t_(down)t_(up)V_(fluid)L_(up) = L_(down) L(t_(up) − t_(dn)) = 2V_(fluid)t_(up)t_(down)$V_{fluid} = \frac{L\left( {t_{up} - t_{down}} \right)}{2t_{up}t_{down}}$

Knowing the velocity of the fluid allows the volume fluid flow(Q_(fluid)) to be determined, where C_(d) is a predetermined dischargecoefficient of the fluid in the fluid control conduit 520:

Q _(fluid) =C _(d) ×A×V _(fluid)

Fluid sound speed properties can also be determined. Since the fluidvelocity is shared between the pair of transducers the fluid velocitycan be solved for. Recalling that:

$t_{up} = \frac{L_{up}}{\left( {C_{fluid} - V_{fluid}} \right)}$ And:$t_{down} = \frac{L_{down}}{\left( {C_{fluid} + V_{fluid}} \right)}$Solvingt_(up)andt_(down)forV_(fluid):V_(fluid) = (L_(down) − t_(down)C_(fluid))/t_(down)V_(fluid) = (−L_(up) + t_(up)C_(fluid))/t_(up)

Since velocity of the fluid is common between the transducers, theprevious two equations equal one another and allow fluid sound speed tobe solved:

V_(fluid) = V_(fluid)$\frac{\left( {L_{down} - {t_{down}C_{fluid}}} \right)}{t_{down}} = \frac{\left( {{- L_{up}} + {t_{up}C_{fluid}}} \right)}{t_{up}}$L_(down)t_(up) − t_(down)t_(up)C_(fluid) = −L_(up)t_(down) + t_(up)t_(down)C_(fluid)L_(down)t_(up) + L_(up)t_(down) = t_(up)t_(down)C_(fluid) + t_(down)t_(up)C_(fluid)L_(up) = L_(down) L(t_(up) + t_(down)) = −2C_(fluid)t_(up)t_(down)$C_{fluid} = \frac{L\left( {t_{up} + t_{down}} \right)}{2t_{up}t_{down}}$

FIGS. 6A and 6B are graphs that show example incident waves and echoesin the ultrasonic flow measurement system of FIG. 1. FIG. 6A shows agraph 600 of acoustic amplitude over time, including a sub-duration 601.FIG. 6B shows a graph 602 in which the sub-duration 601 has beenexpanded for visibility.

The graph 600 shows a representation of the emission of an initialincident wave 610 (e.g., when the acoustic transceiver element 230 isactivated to send an acoustic “ping”). An echo 620 is received a fewmicroseconds later. In some implementations, the echo 620 can be theecho 320 of FIG. 3, which is a reflection of a portion of the incidentwave 310 off the face 274 at the cavity 204.

An echo 630 is received a few microseconds later. In someimplementations, the echo 630 can be the echo 340, which is a reflectionof a portion of the incident wave 330 off the axial end 254, which isalso an interface to the fluid. Echoes 640 represent reverberations inthe buffer rods 250 and 270. In operation, the echoes 640 can befiltered out or otherwise ignored.

An incident wave 670 represents a portion of the incident wave that isreceived by an acoustic sensor (e.g., the acoustic transceiver element230 located downstream or otherwise opposite the acoustic transceiverelement 230 that transmitted the incident wave). The amount of timetaken by the incident wave 670 to arrive is affected by severalvariables, such as the fluid density, flow rate, and flow direction ofthe fluid in the fluid control conduit 130, and the distance 150. Theamount of time taken for the incident wave 670 can be used as t_(up) ort_(down) (e.g., depending on whether the wave travelled upstream ordownstream in the fluid control conduit 130).

As illustrated in FIG. 4, the buffer rod 250 is designed to transferpressure-induced forces to the face 210 of the sensor housing 202. Thisis achieved through the diameter construction of the buffer rod 250,where the smaller cross-sectional area of the acoustic transceiverelement 230 decouples thermal expansion of the sensor housing 202 fromthe acoustic path. The larger cross-sectional area of the axial bufferrod 250 is sized to accommodate the pressure-induced forces acting onthe buffer rod 250. The transmission of forces into the sensor housing202 substantially eliminates pressure-induced forces from acting on theacoustic transceiver element 230 and substantially eliminates the needfor (e.g., piezo ceramic) pressure compensation, sizing to react thepressure induced forces, and substantially avoids wetted transducerdesign constraints.

By decoupling the acoustic transceiver element 230 from the fluidpressure environment, several advantages are observed. For example,fluid/fuel compatibility of the acoustic transceiver element 230 is notrequired, the acoustic transceiver element 230 frequency is notrestricted by thickness requirements driven by pressure induced forces,the thickness of the acoustic transceiver element 230 required tosupport fluid pressure puts operating frequency far below operatingrequirements of time of flight measurement, and acoustic transducerfrequency can be sized for acoustic optimization and low flowmeasurement accuracy.

For aircraft turbine fuel systems, mass fuel flow rate can be determinedfor an understanding of combustion energy content. This is solvedthrough the use of the buffer rods 250 and 270. The designs andarrangement of the buffer rods 250 and 270 enables additional acousticbenefits which can be intentionally designed into the USFM system 100.For example, the configuration of the buffer rods 250 and 270 enablesthe controller 190 to determine reflection coefficients for fuelacoustic impedance measurement. This is achieved by introducing atransducer transmit amplitude response (e.g., echoes 320 or 620),achieved with the cavity 204 which acts as a substantially idealreflector, and this amplitude can be compared to the return echoes ofthe buffer rod fluid interface (e.g., echoes 340 or 630). In someembodiments, the sensitivity of the axial end 254 is further enhanced bythe matching layer 280, however, this will be ignored in order tosimplify the equations below.

Fluid acoustic impedance can be determined by setting echo reflectioneffective areas equal to one another, for example by configuring thecross-sectional areas 209 a and 209 b appropriately. In someimplementations, the areas can be non-equal, and a mathematicalcompensation can be integrated into the process. However, for the sakeof clarity, the areas are assumed to be equal in the equations below.This allows for direct measurement of the reflection coefficient. Thewave propagation within the buffer rod 250 is articulated such that inair, the echo returned from the face 274 is equivalent to the echo fromthe axial end 254.

The reflection coefficient is found through the use of short timeFourier transforms (STFT). The fast Fourier transforms (FFT) of the twoechoes are found to determine the peak of the return echoes:

STFT→Amplitude=f (Frequency)

Therefore:

|A|=|FFT (Echo₁)|_(f=f) ₀

|B|=|FFT(Echo₂)|_(f=f) ₀

Where:

Echo₁ is one of the echoes 320 or 620 of FIGS. 3, 6A, and 6Brespectively, Echo₂ is one of the echoes 340 or 630 of FIGS. 3, 6A, and6B respectively, and f and f₀ are the transducer driving frequency. Thereflection coefficient is then found from:

$R = \frac{❘A❘}{❘B❘}$

And, assuming the buffer rod 250 is in direct interface with the fluidor fuel (e.g., no matching layer 280 in this case):

$R = \frac{Z_{2} - Z_{1}}{Z_{2} + Z_{1}}$

Where R is the reflection coefficient.

Z ₂ =Z _(fluid)

Z ₁ =Z _(buffer)

In some examples, the buffer rod may have properties change withtemperature, which can result in a Z_(buffer) term that is a function oftemperature. These changes can be compensated through temperaturecharacterization of the buffer rod and use of a temperature-sensingdevice located in the system, or temperature references can bedetermined from buffer reflection timing.

$Z_{fluid} = \frac{Z_{buffer}\left( {1 - R} \right)}{1 + R}$

The impedance of the buffer rod 250 can be determined throughcharacterization at the sensor level. With the buffer rod impedanceknown and the reflection coefficient being measured, the fluid impedancecan now be solved for:

Z _(fluid)=ρ_(fluid) ×C _(fluid)

From the equations above, a speed of sound in fluid was solved for.Since fluid impedance and fluid sound speed are known, fluid density cannow be solved for.

$\rho_{fluid} = \frac{Z_{fluid}}{C_{fluid}}$

Explicitly:

$\rho_{fluid} = \frac{\left( \frac{z_{{buffer}^{{({1 - R})})}}}{1 + R} \right)}{\left( \frac{L\left( {t_{up} + t_{down}} \right)}{2t_{up}t_{down}} \right)}$

With volumetric fluid flow and density now known, the mass fluid flowrate can be found:

${\overset{.}{m}}_{fluid} = {{Q_{{fluid} \times}\rho_{fluid}} = {C_{d} \times A \times V_{fluid}\frac{Z_{fluid}}{C_{fluid}}}}$

In another implementation, mass fluid flow can be determined usinganother technique. The derivation below is based on a simplifyingassumption that the transducer faces (e.g., piezo electrical ceramic andtransducers) are all arranged perpendicular to the axis of the fluidduct. Therefore, the below derivation omits angles of incidence. Inexamples in which the piezo transducers were placed off axis, thefollowing derivation could be re-derived to include an angle ofincidence. However, for simplicity such angles have been ignored here.

Mass fuel flow sensing can be achieved by implementing two ultrasonictransducers per channel, in which each transducer sends and receives anacoustic signal. The signals used for mass fuel flow sensing can bebased on time transits upstream and downstream (e.g., for velocity), andinternal transducer reflections (e.g., for impedance sensing).

Q_(fluid) = V_(fluid) × C_(d) × A$\overset{.}{{\overset{.}{m}}_{fluid} = {{Q_{fluid} \times \rho_{fluid}} = {V_{fluid} \times C_{d \times} \times A \times \rho_{fluid}}}}$z = ρ_(fluid) × C_(fluid)${\therefore\rho_{fluid}} = \frac{C_{fluid}}{C_{d}}$$\overset{.}{{\overset{.}{m}}_{fluid} = {{V_{fluid} \times C_{d \times} \times A \times \rho_{fluid}} = \left( \frac{V_{fluid}}{C_{fluid}} \right)}} \times C_{d} \times A \times Z_{fluid}$${\overset{.}{m}}_{fluid} = {{V_{fluid} \times A \times \rho_{fluid}} = {\left( \frac{V_{fluid}}{C_{fluid}} \right) \times C_{d} \times A \times Z_{fluid}}}$${\overset{.}{m}}_{fluid} = {\left( \frac{t_{up} - t_{down}}{t_{up} + t_{down}} \right) \times C_{d} \times A \times Z_{fluid}}$

Where C_(d) and K are commonly interchangeable in literature as a flowcorrection factor:

$\overset{.}{{\overset{.}{m}}_{fluid} = {{V_{fluid} \times A \times \rho_{fluid}} = \left( \frac{V_{fluid}}{C_{fluid}} \right)}} \times K \times A \times Z_{fluid}$${\overset{.}{m}}_{fluid} = {\left( \frac{t_{up} - t_{down}}{t_{up} + t_{down}} \right) \times K \times A \times Z_{fluid}}$

First:

Distance = Velocity × time OrLength(L) = Soundspeed(C_(fluid)) × time(t) ∴ L₁ = C_(fluid) × t₁$t_{1} = \frac{L_{1}}{C_{fluid}}$

Where Cfuel is the speed of sound in fluid, L₁ is the distance betweenthe acoustic transmitter 510 a and the acoustic receiver 512 a, and t₁is the signal transit time between the acoustic transmitter 510 a andthe acoustic receiver 512 a.

Assuming that the direction 501 in which the control volume (fluid) ismoving is the same as a direction of sound travel, represented by line502 a from the acoustic transmitter 510 a to the acoustic receiver 512a, the speed of the sound wave traveling through the fluid will changerelative to the speed of the fluid.

∴ L₂ = C_(fluid) × t₂ V₂ = V_(fluid) + C_(fluid)∴ L₂ = (V_(fluid) + C_(fluid)) × t₂$t_{2} = \frac{L_{2}}{\left( {C_{fluid} + V_{fluid}} \right)}$

Where V_(fluid) is the average velocity of moving fluid, L₂ is thedistance between the acoustic transmitter 510 a and the acousticreceiver 512 a, and t₂ is the signal transit time between the acoustictransmitter 510 a and the acoustic receiver 512 a.

Referring again to FIG. 5B, it is assumed that the control volume(fluid) is opposing the direction of the sound travel from the acousticemitter 510 b to the acoustic receiver 512 b, represented by line 502 b.The speed of the sound wave traveling through the fluid will changerelative to the speed of the fluid.

${{\therefore L_{3}} = {V_{3} \times t_{3}}}{V_{3} = {{- V_{fluid}} + C_{fluid}}}{{\therefore L_{3}} = {\left( {{- V_{fluid}} + C_{fluid}} \right) \times t_{3}}}{t_{3} = \frac{L_{3}}{\left( {C_{fluid} - V_{fluid}} \right)}}$

Where L₃ is the distance between the acoustic emitter 510 b and theacoustic receiver 512 b, and t₃ is the signal transit time between theacoustic emitter 510 b and the acoustic receiver 512 b.

Referring again to FIG. 5C, for a particular set of ultrasonic sensors,and as described above, the devices can both emit and receive signals.This means that for a pair of signals, the following characteristics areshared:

L_(up)=L_(down)=L=distance between emitters;

D=diameter Area of the fluid control conduit 520;

A=cross section area;

C_(fluid)=speed of sound in fluid;

V_(fluid)=velocity of fluid;

P_(fluid)=density of fluid;

Z_(fluid)=Acoustic impedance of fluid.

With the above properties shared, the difference in time between theupstream and downstream signal will allow calculation of various fluidcharacteristics.

Upstream and downstream transit times become:

$t_{up} = \frac{L_{up}}{\left( {C_{fluid} - V_{fluid}} \right)}$$t_{down} = \frac{L_{down}}{\left( {C_{fluid} + V_{fluid}} \right)}$

Solving for t_(up), t_(down), for L:

L _(up) =t _(up) ×C _(fluid) −t _(dn) V _(fluid)

L _(dn) =t _(dn) ×C _(fluid) −t _(dn) ×V _(fluid)

Since length is common between the transducers, L_(up) and L_(dn) areequal to one another and allows fuel velocity to sound speed ratio to befound.

t_(up) × C_(fluid) − t_(up) × V_(fluid) = t_(dn) × C_(fluid) + t_(dn) × V_(fluid)t_(up) × C_(fluid) − t_(dn) × C_(fluid) = t_(dn) × V_(fluid) + t_(dn) × V_(fluid)$\frac{V}{C} = \frac{t_{up} - t_{dn}}{t_{up} + t_{dn}}$$\frac{V_{fluid}}{fluid} = \frac{t_{up} - t_{dn}}{t_{up} + t_{dn}}$

Substituting the preceding equation into the earlier equation for massflow:

${\overset{.}{m}}_{fluid} = {{\left( \frac{V_{fluid}}{C_{fluid}} \right) \times C_{d} \times A \times Z_{fluid}} = {\left( \frac{t_{up} - t_{dn}}{t_{up} + t_{dn}} \right) \times C_{d} \times A \times Z_{fluid}}}$

With the acoustic impedance (Z), the conduit area (A), and the measuredtime transits known, the mass fluid flow can be solved.

As shown above:

$Z_{fluid} = \frac{z_{{buffer}({1 - R})}}{1 + R}$

Substituting the previous mass flow equation in the preceding equation:

${\overset{.}{m}}_{fluid} = {{\left( \frac{V_{fluid}}{C_{fluid}} \right) \times C_{d} \times A \times Z_{fluid}} = {\left( \frac{t_{up} - t_{dn}}{t_{up} + t_{dn}} \right) \times C_{d} \times A \times \left( \frac{z_{{buffer}({1 - R})}}{1 + R} \right)}}$

FIG. 7 is a flow chart that shows an example of a process 700 fordetermining a fluid reflection coefficient. In some implementations, theprocess 700 can be used with the example ultrasonic sensor module 200 ofFIGS. 1-2B.

At 710, a first emitter is activated to emit at a first incident waveand a second incident wave. For example, the example acoustictransceiver element 230 can be activated to emit an indecent wave fromboth of its faces.

At 720 the incident wave is transmitted along a first buffer rod havinga first axial end abutted to the first emitter and a second axial endopposite the first axial end. For example, the first incident wave canpropagate through the buffer rod 250.

At 725 the incident wave is transmitted along a second buffer rod havinga third axial end abutted to the first emitter and a fourth axial endopposite the third axial end. For example, the second incident wave canpropagate through the buffer rod 270.

At 730 a first echo of the first incident wave is reflected by a firstacoustic reflector defined along a portion of the first buffer rod. Forexample, the portion of the incident wave 330 can encounter the face 254and be reflected as the echo 340. In some implementations, the firstecho can be reflected by a ¼ λ matching layer affixed to the secondaxial end, for example, the matching layer 280 at the axial end 254.

At 740, the first echo is detected. For example, the echo 620 of FIGS.6A and 6B can be detected.

At 750 a first amplitude of the first echo is determined. For example, aFFT can be performed on the echo 620 to determine an amplitude of theecho 620 (e.g., amplitude A as described above).

At 760 a second echo of the incident wave is reflected by the fourthaxial end. For example, a portion of the incident wave 310 is reflectedoff the axial end 274 as the echo 320.

At 770, the second echo is detected. For example, the echo 630 of FIGS.6A and 6B can be detected.

At 780, a second amplitude of the second echo is determined. Forexample, a FFT can be performed on the echo 640 to determine anamplitude of the echo 640 (e.g., amplitude B as described above).

At 790, a reflection coefficient based on the first amplitude and thesecond amplitude can be determined. For example:

$R = \frac{❘A❘}{❘B❘}$

FIG. 8 is a flow chart that shows an example of a process 800 fordetermining a mass fluid flow. In some implementations, the process 800can be used with the example USFM system 100 of FIG. 1.

At 805, a reflection coefficient value is received. For example, Forexample, the reflection coefficient R determined at 790 can be received.

At 810, a fluid acoustic impedance of a fluid at the second axial end isdetermined based on the determined reflection coefficient and apredetermined buffer rod acoustic impedance. For example, the reflectioncoefficient R can be used along with the predetermined buffer rodimpedance Z_(buffer) to determine Z_(fluid), as described above.

At 815, a portion of the incident wave is transmitted at the secondaxial end through the fluid to a sensor arranged a predetermineddistance away from and opposite the first emitter, where the fluid iswithin a tubular fluid conduit having a predetermined cross-sectionalarea. For example, the incident wave 670 of FIG. 6A can travel throughthe fluid from the ultrasonic sensor module 200 that is upstream to theultrasonic sensor module 200 that is downstream.

At 820, the second sensor detects the portion of the incident wave. Forexample, the ultrasonic sensor module 200 that is downstream can detectthe incident wave 670.

At 825, a first time of flight of the portion of the incident wave isdetermined based on the detected portion of the incident wave. Forexample, t_(down) can be determined.

At 830, another incident wave is transmitted, by a second emitter,through the fluid to the first sensor. For example, the ultrasonicsensor module 200 that is downstream can be activated to emit anotherindecent wave upstream.

At 835, the first sensor detects the other incident wave, and at 840 asecond time of flight of the other incident wave is determined based onthe detected other incident wave. For example, t_(up) can be determined.

At 845, a velocity of the fluid within the tubular fluid conduit isdetermined.

For example, V_(fluid) can be determined as:

$V_{fluid} = \frac{L\left( {t_{up} - t_{down}} \right)}{2t_{up}t_{down}}$

At 850, a speed of sound within the fluid is determined. For example,C_(fluid) can be determined as:

$C_{fluid} = \frac{L\left( {t_{up} - t_{down}} \right)}{2t_{up}t_{down}}$

At 855, a mass fluid flow rate is determined based on at least thepredetermined cross-sectional area, the determined velocity of thefluid, the determined fluid acoustic impedance, and the determined speedof sound. For example:

${\overset{.}{m}}_{fluid} = {{Q_{fluid}\rho_{fluid}} = {C_{d}{AV}_{fluid}\frac{Z_{fluid}}{C_{fluid}}}}$Or:${\overset{.}{m}}_{fluid} = {{\left( \frac{V_{fluid}}{C_{fluid}} \right) \times C_{d} \times A \times Z_{fluid}} = {\left( \frac{t_{up} - t_{dn}}{t_{up} + t_{dn}} \right) \times C_{d} \times A \times \left( \frac{z_{{buffer}({1 - R})}}{1 + R} \right)}}$

In some implementations, one or both of the first emitter and the firstsensor can be piezo elements. In some implementations, the piezo elementcan include the first emitter and the first sensor. For example, theemitter and sensor can be separate components, or the acoustictransceiver element 230 can perform the emitting and detecting functionswithin the ultrasonic sensor module 200.

FIG. 9 is a flow chart that shows an example of a process 900 forresisting effects of fluid exposure on the acoustic transceiver element230 of the example ultrasonic sensor module 200 of FIGS. 1-4. At 910, asensor is provided. The sensor includes a sensor housing having aninterior surface defining a sensor axis and an axial interior sensorhousing cavity having a first axial sensor housing portion having afirst cross-sectional area perpendicular to the sensor axis, a secondaxial sensor housing portion arranged adjacent to the first axial sensorhousing portion along the sensor axis and having a secondcross-sectional area larger than the first cross-sectional areaperpendicular to the sensor axis, and a face extending from the interiorsurface of the first axial housing portion to the interior surface ofthe second housing portion, a buffer rod having a first axial end and asecond axial end opposite the first axial end and having a first axialbuffer portion arranged within the first housing portion and having thefirst axial end, a second axial buffer portion arranged within thesecond housing portion and abutting the face, and having the secondaxial end, and a third axial buffer portion, extending axially betweenthe first axial buffer portion and the second axial buffer portion, andhaving a third cross-sectional area, smaller than the firstcross-sectional area, perpendicular to the sensor axis, and an acoustictransceiver element acoustically mated to the first end. For example,the ultrasonic sensor module 200 can be provided.

At 920, a fluid is provided at the second axial end. For example, thefluid 301, such as a fuel, can be provided in the fluid cavity 120 a or120 b so as to contact the axial end 254.

At 930, the buffer rod and the sensor housing blocks fluid flow from thesecond end to the acoustic transceiver element. For example, asdiscussed in the description of FIG. 4, the acoustic transceiver element230 is separated from the fluid 301 by the sensor housing 202 and thebuffer rod 250, and the fluid 301 by the sensor housing 202 and thebuffer rod 250 are configured to prevent the fluid 301 from flowing tothe acoustic transceiver element 230.

In some implementations, fluid flow from the second end to the acoustictransceiver element can be blocked by the sensor housing and the secondaxial buffer portion. For example, the fluid 301 is prevented fromflowing to the acoustic transceiver element 230 by interference betweenthe sensor housing 202 and the axial buffer rod 250.

At 940, a fluid pressure is applied against the second axial end toproduce an axial force against the buffer rod. For example, the fluidforce 410 can be applied against the axial end 254.

At 950, the buffer rod transmits the axial force to the sensor housing.For example, the buffer rod 250 transmits the force 420 to the sensorhousing 202.

At 960, the sensor housing prevents transmission of the axial force tothe acoustic transceiver element. In some implementations, the process900 can also include transmitting, by the second axial portion, theaxial force to the face, wherein the face interferes with axial movementof the buffer rod toward the acoustic transceiver element. For example,any movement of the buffer rod 250 into the sensor cavity 204 isprevented by the counteractive force 430 created through contact betweenthe axial buffer rod 250 and the face 210.

FIG. 10 is a schematic diagram of an example of a generic computersystem 1000. The system 1000 can be used for the operations described inassociation with the process 700, 800, and/or 900 according to oneimplementation. For example, the system 1000 may be included in thecontroller 190.

The system 1000 includes a processor 1010, a memory 1020, a storagedevice 1030, and an input/output device 1040. Each of the components1010, 1020, 1030, and 1040 are interconnected using a system bus 1050.The processor 1010 is capable of processing instructions for executionwithin the system 1000. In one implementation, the processor 1010 is asingle-threaded processor. In another implementation, the processor 1010is a multi-threaded processor. The processor 1010 is capable ofprocessing instructions stored in the memory 1020 or on the storagedevice 1030 to display graphical information for a user interface on theinput/output device 1040.

The memory 1020 stores information within the system 1000. In oneimplementation, the memory 1020 is a computer-readable medium. In oneimplementation, the memory 1020 is a volatile memory unit. In anotherimplementation, the memory 1020 is a non-volatile memory unit.

The storage device 1030 is capable of providing mass storage for thesystem 1000. In one implementation, the storage device 1030 is acomputer-readable medium. In various different implementations, thestorage device 1030 may be a floppy disk device, a hard disk device, anoptical disk device, or a tape device.

The input/output device 1040 provides input/output operations for thesystem 1000. In one implementation, the input/output device 1040includes a keyboard and/or pointing device. In another implementation,the input/output device 1040 includes a display unit for displayinggraphical user interfaces.

The features described can be implemented in digital electroniccircuitry, or in computer hardware, firmware, software, or incombinations of them. The apparatus can be implemented in a computerprogram product tangibly embodied in an information carrier, e.g., in amachine-readable storage device for execution by a programmableprocessor; and method steps can be performed by a programmable processorexecuting a program of instructions to perform functions of thedescribed implementations by operating on input data and generatingoutput. The described features can be implemented advantageously in oneor more computer programs that are executable on a programmable systemincluding at least one programmable processor coupled to receive dataand instructions from, and to transmit data and instructions to, a datastorage system, at least one input device, and at least one outputdevice. A computer program is a set of instructions that can be used,directly or indirectly, in a computer to perform a certain activity orbring about a certain result. A computer program can be written in anyform of programming language, including compiled or interpretedlanguages, and it can be deployed in any form, including as astand-alone program or as a module, component, subroutine, or other unitsuitable for use in a computing environment.

Suitable processors for the execution of a program of instructionsinclude, by way of example, both general and special purposemicroprocessors, and the sole processor or one of multiple processors ofany kind of computer. Generally, a processor will receive instructionsand data from a read-only memory or a random access memory or both. Theessential elements of a computer are a processor for executinginstructions and one or more memories for storing instructions and data.Generally, a computer will also include, or be operatively coupled tocommunicate with, one or more mass storage devices for storing datafiles; such devices include magnetic disks, such as internal hard disksand removable disks; magneto-optical disks; and optical disks. Storagedevices suitable for tangibly embodying computer program instructionsand data include all forms of non-volatile memory, including by way ofexample semiconductor memory devices, such as EPROM, EEPROM, and flashmemory devices; magnetic disks such as internal hard disks and removabledisks; magneto-optical disks; and CD-ROM and DVD-ROM disks. Theprocessor and the memory can be supplemented by, or incorporated in,ASICs (application-specific integrated circuits), or FPGA (FieldProgrammable Gate Arrays, with or without embedded processing elements).

To provide for interaction with a user, the features can be implementedon a computer having a display device such as a CRT (cathode ray tube)or LCD (liquid crystal display) monitor for displaying information tothe user and a keyboard and a pointing device such as a mouse or atrackball by which the user can provide input to the computer.

The features can be implemented in a computer system that includes aback-end component, such as a data server, or that includes a middlewarecomponent, such as an application server or an Internet server, or thatincludes a front-end component, such as a client computer having agraphical user interface or an Internet browser, or any combination ofthem. The components of the system can be connected by any form ormedium of digital data communication such as a communication network.Examples of communication networks include, e.g., a LAN, a WAN, and thecomputers and networks forming the Internet.

The computer system can include clients and servers. A client and serverare generally remote from each other and typically interact through anetwork, such as the described one. The relationship of client andserver arises by virtue of computer programs running on the respectivecomputers and having a client-server relationship to each other.

Although a few implementations have been described in detail above,other modifications are possible. In addition, the logic flows depictedin the figures do not require the particular order shown, or sequentialorder, to achieve desirable results. In addition, other steps may beprovided, or steps may be eliminated, from the described flows, andother components may be added to, or removed from, the describedsystems. Accordingly, other implementations are within the scope of thefollowing claims.

What is claimed is:
 1. A sensor comprising: a sensor housing having aninterior surface defining a sensor axis and an axial interior sensorhousing cavity comprising: a first axial sensor housing portion having afirst cross-sectional area perpendicular to the sensor axis; a secondaxial sensor housing portion arranged adjacent to the first axial sensorhousing portion along the sensor axis and having a secondcross-sectional area larger than the first cross-sectional areaperpendicular to the sensor axis; and a face extending from the interiorsurface of the first axial sensor housing portion to the interiorsurface of the second axial sensor housing portion; a first axial bufferrod arranged within the first axial sensor housing portion andcomprising a first axial end and a second axial end; a second axialbuffer rod arranged within the second axial sensor housing portion andabutting the face, and comprising a third axial end and a fourth axialend; and an acoustic transceiver element acoustically mated to thesecond axial end and the third axial end.
 2. The sensor of claim 1,wherein the acoustic transceiver element is configured to emit avibration having a predetermined wavelength (λ), and the first axialbuffer rod and the second axial buffer rod both have axial lengths ofabout a round multiple of n/2 λ.
 3. The sensor of claim 1, furthercomprising a tubular fluid conduit having a first end and a second endopposite the first end and defining a conduit axis, arranged such thatthe conduit axis is substantially aligned with the sensor axis.
 4. Thesensor of claim 3, further comprising: another sensor housing havinganother interior surface defining another sensor axis and another axialinterior sensor housing cavity comprising: another first axial sensorhousing portion having another first cross-sectional area perpendicularto the other sensor axis; another second axial sensor housing portionarranged adjacent to the other first axial sensor housing portion alongthe other sensor axis and having another second cross-sectional arealarger than the other first cross-sectional area perpendicular to theother sensor axis; and another face extending from the other interiorsurface of the other first axial housing portion to the other interiorsurface of the other second housing portion; another first axial bufferrod arranged within the other first housing portion and comprisinganother first axial end and another second axial end; another secondaxial buffer rod arranged within the other second housing portion andabutting the other face, and comprising another third axial end andanother fourth axial end; and another acoustic transceiver elementacoustically mated to the other second axial end and the other thirdaxial end; wherein the other sensor axis is substantially aligned withthe conduit axis.
 5. The sensor of claim 3, further comprising: a fluidhousing comprising: a fluid housing interior surface defining an axialfluid housing cavity; a first fluid port in fluidic communication withthe axial fluid housing cavity; and a second fluid port in fluidiccommunication with the axial fluid housing cavity; wherein the tubularfluid conduit is in fluidic communication with the second fluid port andextends axially away from the fluid housing along the conduit axis atthe first end, and the sensor housing is arranged within the first fluidhousing such that the sensor axis is substantially aligned with theconduit axis.
 6. The sensor of claim 5, further comprising: anothersensor housing having another interior surface defining another sensoraxis and another axial interior sensor housing cavity comprising:another first axial sensor housing portion having another firstcross-sectional area perpendicular to the other sensor axis; anothersecond axial sensor housing portion arranged adjacent to the other firstaxial sensor housing portion along the other sensor axis and havinganother second cross-sectional area larger than the other firstcross-sectional area perpendicular to the other sensor axis; and anotherface extending from the other interior surface of the other first axialhousing portion to the other interior surface of the other secondhousing portion; another first axial buffer rod arranged within theother first housing portion and comprising another first axial end andanother second axial end; another second axial buffer rod arrangedwithin the other second housing portion and abutting the other face, andcomprising another third axial end and another fourth axial end; anotheracoustic transceiver element acoustically mated to the other secondaxial end and the other third axial end; and another fluid housingcomprising: another fluid housing interior surface defining anotheraxial fluid housing cavity; another first fluid port in fluidiccommunication with the other axial fluid housing cavity; and anothersecond fluid port in fluidic communication with the other axial fluidhousing cavity; wherein the tubular fluid conduit is in fluidiccommunication with the other second fluid port and extends axially awayfrom the other fluid housing along the conduit axis at the second end,and the other sensor housing is arranged within the other first fluidhousing such that the other sensor axis is substantially aligned withthe conduit axis.
 7. The sensor of claim 1, wherein the acoustictransceiver element comprises a piezoelectric element.
 8. The sensor ofclaim 1, further comprising a matching layer affixed to the fourth axialend and having a thickness of about (2n−1)λ/4, where n>0.
 9. The sensorof claim 1, wherein the first axial end defines an acoustic reflector.10. The sensor of claim 1, wherein the first axial end is abutted to agas or an at least partial vacuum.
 11. A sensor system comprising: afluid housing comprising: a first fluid housing portion defining a firstaxial fluid housing cavity and comprising a first fluid port in fluidiccommunication with the first axial fluid housing cavity; a second fluidhousing portion defining a second axial fluid housing cavity andcomprising a second fluid port in fluidic communication with the secondaxial fluid housing cavity; and a tubular fluid conduit in fluidiccommunication with the first fluid port at a first end and in fluidiccommunication with the second fluid port at a second end opposite thefirst end, and defining a conduit axis; a first acoustic transceiverelement arranged within the first axial fluid housing cavity, axiallyaligned with the conduit axis; and a second acoustic transceiver elementarranged within the second axial fluid housing cavity, axially alignedwith the conduit axis.
 12. The sensor system of claim 11, furthercomprising circuitry configured to: activate the first acoustictransceiver element to emit a first incident wave; activate the secondacoustic transceiver element to emit a second incident wave; detect, bythe first acoustic transceiver element, an echo of the first incidentwave; determine a fluid acoustic impedance of a fluid in the tubularfluid conduit based on the echo; detect, by the second acoustictransceiver element, at least a first portion of the first incidentwave; determine a first time of flight of the portion of the firstportion; detect, by the first acoustic transceiver element, at least asecond portion of the second incident wave; determine a second time offlight of the second portion; and determine a mass fluid flow rate basedon the determined fluid acoustic impedance, the determined first time offlight, and the determined second time of flight.
 13. The sensor systemof claim 11, wherein one or both of the first acoustic transceiverelement or the second acoustic transceiver element each comprises: asensor housing having an interior surface defining a sensor axis and anaxial interior sensor housing cavity comprising: a first axial sensorhousing portion having a first cross-sectional area perpendicular to thesensor axis; a second axial sensor housing portion arranged adjacent tothe first axial sensor housing portion along the sensor axis and havinga second cross-sectional area larger than the first cross-sectional areaperpendicular to the sensor axis; and a face extending from the interiorsurface of the first axial sensor housing portion to the interiorsurface of the second axial sensor housing portion; a first axial bufferrod arranged within the first axial sensor housing portion andcomprising a first axial end and a second axial end; a second axialbuffer rod arranged within the second axial sensor housing portion andabutting the face, and comprising a third axial end and a fourth axialend; and an acoustic transceiver element acoustically mated to thesecond axial end and the third axial end.
 14. The sensor system of claim13, wherein the acoustic transceiver element is configured to emit avibration having a predetermined wavelength (λ), and the first axialbuffer rod and the second axial buffer rod both have axial lengths ofabout a round multiple of n/2 λ.
 15. The sensor of claim 13, wherein theacoustic transceiver element comprises a piezo element.
 16. The sensorsystem of claim 13, further comprising a matching layer affixed to thefourth end and having a thickness of about an odd multiple of ¼λ. 17.The sensor system of claim 13, wherein the first axial end defines anacoustic reflector.
 18. The sensor system of claim 13, wherein the firstaxial end is abutted to a gas or an at least partial vacuum.
 19. Amethod of sensing, comprising: activating a first emitter to emit atleast a first incident wave in a first direction and emit a secondincident wave in a second direction opposite the first direction;transmitting the first incident wave along a first buffer rod having afirst axial end abutted to the first emitter and a second axial endopposite the first axial end; transmitting the second incident wavealong a second buffer rod having a third axial end abutted to the firstemitter and a fourth axial end opposite the third axial end; reflectinga first echo of the first incident wave by a first acoustic reflectordefined along a portion of the second axial end; detecting the firstecho; determining a first amplitude of the first echo; reflecting asecond echo of the second incident wave by the fourth axial end;detecting the second echo; determining a second amplitude of the secondecho; and determining a reflection coefficient based on the firstamplitude and the second amplitude.
 20. The method of claim 19, furthercomprising determining a fluid acoustic impedance of a fluid at thesecond axial end based on the determined reflection coefficient and apredetermined buffer rod acoustic impedance.
 21. The method of claim 20,further comprising: transmitting, at the second axial end, a portion ofthe first incident wave through the fluid to a first sensor arranged apredetermined distance away from and opposite the first emitter, whereinthe fluid is within a tubular fluid conduit having a predeterminedcross-sectional area; detecting, by the first sensor, the portion of thefirst incident wave; determining, based on the detected portion of thefirst incident wave, a first time of flight of the portion of the firstincident wave; transmitting, by a second emitter, another first incidentwave through the fluid to a second sensor proximal to the first emitter;detecting, by the second sensor, the other first incident wave; anddetermining, based on the detected other first incident wave, a secondtime of flight of the other first incident wave.
 22. The method of claim21, further comprising determining at least one of a velocity of thefluid within the tubular fluid conduit or a speed of sound within thefluid based on the first time of flight, the second time of flight, andthe predetermined distance.
 23. The method of claim 22, furthercomprising determining a mass fluid flow rate based on the predeterminedcross-sectional area, and the determined speed of sound.
 24. The methodof claim 23, wherein the mass fluid flow rate is given by the equation${\overset{˙}{m}}_{fluid} = {{\left( \frac{V_{fluid}}{C_{fluid}} \right) \times C_{d} \times A \times Z_{fluid}} = {{\left( \frac{t_{up} - t_{dn}}{t_{up} + t_{dn}} \right) \times C_{d} \times A \times \left( \frac{z_{buffer}\left( {1 - R} \right)}{1 + R} \right)}\therefore}}$25. The method of claim 21, wherein one or both of the first emitter andthe first sensor are piezo elements.
 26. The method of claim 21, whereina piezo element comprises the first emitter and the first sensor. 27.The method of claim 19, wherein the first acoustic reflector comprises amatching layer affixed to the fourth axial end and having a thickness of(2n−1) λ/4, where n>0.
 28. The method of claim 19, wherein the firstaxial end is abutted to a gas or an at least partial vacuum.
 29. Amethod of protecting a sensor element, comprising: providing a sensorcomprising: a sensor housing having an interior surface defining asensor axis and an axial interior sensor housing cavity comprising: afirst axial sensor housing portion having a first cross-sectional areaperpendicular to the sensor axis; a second axial sensor housing portionarranged adjacent to the first axial sensor housing portion along thesensor axis and having a second cross-sectional area larger than thefirst cross-sectional area perpendicular to the sensor axis; and a faceextending from the interior surface of the first axial sensor housingportion to the interior surface of the second axial sensor housingportion; a first axial buffer rod arranged within the first axial sensorhousing portion and comprising a first axial end and a second axial end;a second axial buffer rod arranged within the second axial sensorhousing portion and abutting the face, and comprising a third axial endand a fourth axial end; and an acoustic transceiver element acousticallymated to the second axial end and the third axial end; providing a fluidat fourth axial end; and blocking, by the second axial buffer rod andthe sensor housing, fluid flow from the fourth axial end to the acoustictransceiver element.
 30. The method of claim 29, further comprising:applying fluid pressure against the fourth axial end to produce an axialforce against the second axial buffer rod; transmitting, by the secondaxial buffer rod, the axial force to the sensor housing; and preventing,by the sensor housing, transmission of the axial force to the acoustictransceiver element.
 31. The method of claim 30, further comprisingtransmitting, by the second axial portion, the axial force to the face,wherein the face interferes with axial movement of the second axialbuffer rod toward the acoustic transceiver element.